A markov-chain model for multivariate magazine-exposure distributions

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Abstract

A multivariate magazine-exposure model that generalizes Danaher’s univariate model is developed. Let Si be the number of issues of magazine/a person reads (Si = 0, 1,…, ki i = 1,…. m). My Markov-chain model considers both within- and between-magazine correlation with the result that S1…, Sm are conditionally independent given the reading outcome for the first issue of each magazine. I am ultimately interested in modeling ST = S„ the total number of exposures a person has to a set of magazines, and I derive this from the model for the joint distribution of (S1…, Sm). The proposed model is shown to give a significantly better fit to observed exposure distributions than the best currently known models. Finally, I obtain the asymptotic distribution of Sr, which can be used for advertising schedules with many magazines and has the benefit of being computationally much faster than my exact model.

Original languageEnglish
Pages (from-to)401-407
Number of pages7
JournalJournal of Business and Economic Statistics
Volume10
Issue number4
DOIs
Publication statusPublished - 1 Jan 1992
Externally publishedYes

Keywords

  • Beta-binomial
  • Canonical expansion

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